Find the inverse of the matrix A = [2 5; 1 3]. a. [3 -5; -1 2] b. [3 -1; -5 2] c. [2 -5; 1 3] d. [3 1; -5 2]
Question
Find the inverse of the matrix A = [2 5; 1 3].
a. [3 -5; -1 2]
b. [3 -1; -5 2]
c. [2 -5; 1 3]
d. [3 1; -5 2]
Solution
The inverse of a 2x2 matrix [a b; c d] is given by 1/(ad-bc) * [d -b; -c a].
So, for the matrix A = [2 5; 1 3], the determinant (ad-bc) is (23 - 51) = 1.
Therefore, the inverse of A is 1/1 * [3 -5; -1 2], which simplifies to [3 -5; -1 2].
So, the correct answer is:
a. [3 -5; -1 2]
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